1. Field of the Invention
The present invention relates generally to a process for optimizing the control parameters of a system by measuring differences between an actual behavior and a desired behavior.
2. Description of the Related Art
In modern manufacturing equipment, for reasons of cost, time and staff savings, manufacturing systems are frequently employed which are very complex and the correct functioning of which is dependent on a multiplicity of control parameters. It is particularly important here that such control parameters that bring about a correct actual behavior in relation to the reference behavior of such a system are available as a function of time. This means that the parameters must be such that the actual behavior of the system corresponds as closely as possible to the reference behavior.
Some examples of such systems are:
Robot arms which move a tool, such as a laser or burr removing tool, for example, which is to be guided along a particular contour line of a workpiece. PA1 Heating systems which are intended to impart a particular temperature profile to a workpiece. PA1 a) wherein in a first step a trainable component is taught the actual behavior of the system, PA1 b) wherein in a second step the difference between reference behavior and actual behavior of the system, as reference deviation, is determined as a function of the control parameters and is supplied to at least one trainable component to which the actual behavior of the system has been taught, and the component provides a correction value for the control parameters corresponding to the reference deviation, PA1 c) wherein in a third step new control parameters are determined with the aid of the correction value in such a way that they bring about an improvement of the actual behavior with respect to the reference behavior of the system, and PA1 d) wherein at least the steps b) and c) are performed until the difference between reference behavior and actual behavior of the system falls below a predetermined value.
In order to be able to control such systems, it is necessary to know and describe their response characteristics very precisely. For control one can attempt to record the response characteristics of the systems in higher-order differential equations. In the case of mechanical systems, such as a robot arm for example, the differential equation would be influenced by the weight of the tool, the weight of the individual arms, the moments of inertia that occur during movements, the torques of the motors and the manner in which the individual joints and the sections of the robot arm connected thereto are positioned. It is already evident from the above that a very complex differential equation would result with the known variables. A further complicating factor is the fact that the systems, such as a robot arm for example, exhibit nonlinearities. The nonlinearities consist, for example, of the play in the joints, of the play in the speed-transforming transmissions and of the positioning imprecision of the servos. These variables are not predictable and therefore cannot be described either.
Analogously, other nonlinearities are conceivable in the case of heating controllers, such as, for example, the thermal conductivity coefficient of the insulation, the different reflection behavior of the heated material, convection influences, different ambient temperatures, etc.
In order to be able to employ such expensive investment goods, such as robots for example, in the production process for as long as possible, there are methods for determining the parameters of these systems without using a robot. In the case of robot arms which guide tools, for example, it is necessary to specify coordinates along which the robot is to guide the tool. A travel trajectory is then produced by the chronological sequence of the coordinates. One method for determining such xy coordinates is, for example, that of simulating a robot arm. In this case the model of a robot arm containing all the known variables of the robot arm is described in a computer. This description includes, for example, the geometry, the kinematic and the dynamic behavior of the robot, of the workpieces and of the machines, and also the behavior of the sensors where they are relevant to the simulation.
It is also particularly important in this connection that the control behavior of the robot is also taken into account in such simulation models.
Control parameters are then supplied to the model, xy coordinates in the case of a robot arm and possibly also z coordinates of a travel trajectory. The actual behavior of the robot arm then becomes apparent from the simulation, which can then be compared with the known reference behavior, namely the coordinates of the trajectory. The control parameters, that is to say the coordinates for the robot model, can be optimized on the basis of this comparison.
It is then possible to drive the real robot with the control parameters optimized on the model in this way. As a result of the aforesaid nonlinearities it will not have the reference behavior, that is to say the reference trajectory will be described more or less precisely by the robot arm. It is then necessary for a person to optimize the coordinates, that is to say the control parameters, for the real robot in a time-consuming process. In the case of laser cutting and burr removal, for example, this also involves the use of a large amount of material since real workpieces are machined. Another method of teaching robot arms travel trajectories is the direct teach-in process, in which the individual coordinates lying on the trajectory that the robot is to describe during the manufacturing process are approached point-by-point, and after all the coordinate points have been entered the person also optimizes the dynamic behavior and specifies the control parameters accordingly.
It would be a great advantage if this step of control parameter optimization could also be automated. Conventional methods of speeding up this optimization process are aimed at improving the control of the robot.
Two of the most important techniques are the "Nonlinear Control" theory and the "Computed Torque" method. With respect to the first group, Casareo and Mariano and Spong describe a linearized feedback, and Freund proposes a nonlinear transformation for decoupling the nonlinearities of the robot dynamics. They all assume that the inertia matrix is fully known. A very exact robot model is therefore required for these techniques.
If a model of robot dynamics in real-time along a desired trajectory can be calculated, then the drive moments for each joint can be recalculated for each instruction transferred from the robot controller. This is referred to as the "Computed Torque" or "Inverse Dynamics" method. As a result of the difficulty of modeling, errors caused by play and friction in the joints, different loading or inertia effects cannot be avoided.
A further technique is the so-called "Model Reference Adaptive Control". With this adaptive process, control is executed in such a way that the difference between the actual behavior calculated with a model (second-order damped system) and the current actual behavior of the robot is minimized. Owing to the fact that the comparison is with a model and not with the desired trajectory, errors inevitably occur if the model is not very exact.
In order to reduce these errors Arimoto and others have presented a new method termed "Learning Control". Analogously to this technique, Potthast and Tio determine the parameters of an inverse linear system model based on the comparison between the input and output signal of a CNC machine. Using the inverse system model, the CNC program (input signal, control parameters) is subsequently modified before execution in such a way that the output signal matches the desired trajectory. With this process the original control parameters have to be modified before every execution. Errors in the system model also lead to deviations from the reference behavior.
The inclusion of nonlinearities in the model is seen as a suitable step in the direction of improving the system model. D. Psaltis et al. (the publication by D. Psaltis, A. Sideris, and A. Yamamura, entitled Neural Controllers, Proc. IEEE First Int'l. Conf. Neural Networks, San Diego, Calif., June 21-24, pp. 51-58, (1987) and the publication by D. Psaltis, A. Sideris and A. Yamamura entitled A Multilayered Neural Network Controller, IEEE Control Systems Magazine 8, pp.17-21 (1988)) use for this purpose a multilayer neural network that can be trained on-line.
W. T. Miller III et al. (the publication by W. T. Miller III, F. H. Glanz and L. G. Kraft III entitled Application of General Learning to the Control of Robotic Manipulators, The Int. J. of Robotics Research 6, pp.84-98 (1987), the publication by W. T. Miller III entitled Real-time Application of Neural Networks for Sensor-based Control of Robots with Vision, IEEE Trans. SMC 19, pp.825-831 (1989), and the publication by W. T. Miller III, R. P. Howes, F. H. Glanz and L. G. Kraft III entitled Real-time Control of an Industrial Manipulator using a Neural-Network-based Learning Controller, IEEE Trans. Robotics and Automation 6, pp.1-9 (1990)) use an approximation model of the robot dynamics valid only for specific regions of the working area, for which a neural network is trained. The learning rule applied is similar to the Widrow-Hoff learning rule for adaptive elements.
Further processes for optimizing control parameters for a system having an actual behavior depending on the control parameters which in particular do not affect the control of the system are not known.